This award supports theoretical research and computational modeling, and education with an aim to better understand ferroelectrics, which are multifunctional materials that have many uses, including actuators, sensors, memory storage, and microelectromechanical systems. These materials can not only produce electric signals under an applied electric field or a macroscopic shape deformation under an applied mechanical stress field but can also produce electric signals in response to an applied mechanical stress or a shape deformation in response to an applied electric field. There have been extensive studies on the couplings among electric signals, electric fields, homogeneous mechanical loads, temperature, and homogeneous shape deformations, and the basic science of how a homogeneous shape deformation affects the electric properties of ferroelectrics, characterized by the "piezoelectric effect," is reasonably well understood. In this project, the PI will focus on understanding how an inhomogeneous stress or shape deformation affects the multifunctional properties of ferroelectrics, through the "flexoelectric effect." Effort will be devoted to developing efficient computational methods and employing them to model, predict, and understand internal, nanoscale inhomogeneous structures and properties of ferroelectric materials under the influence of the flexoelectric effect. The computational research will be carried out in close collaboration with numerous experimental groups, computational physicists, and applied mathematicians. The fundamental understanding achieved and the computational tools developed in this project should provide guidance to develop material systems that can exploit the flexoelectric effect that exists in all materials. The proposed research is expected to contribute to graduate education in materials as phase-field simulations of phase transformations and microstructure evolution are being incorporated into graduate courses at Penn State. In particular, user-friendly graphical interfaces for a number of applications of the phase-field models have been developed under prior NSF support. The software has been employed in two graduate courses and one undergraduate course. In addition, it has been used in summer short courses on computational thermodynamics and kinetics of phase transformations, which were offered to research scientists from national labs, engineers from industry, and professors and students from academia. This project will provide new computational tools to illustrate how materials properties may be modified through the flexoelectric effect. The PI will involve undergraduate students in the research by participating in a number of programs at Penn State including senior thesis projects and the Minority Undergraduate Research Experience program.
Ferroelectrics are a class of materials in which a spontaneous electric polarization develops below their paraelectric to ferroelectric phase transition temperatures. The spontaneous polarization direction can be reoriented among crystallographically defined orientations in a single crystal by an electric field. Very often a spontaneous strain arising from the crystal structure change at the ferroelectric transition accompanies the appearance of spontaneous polarization. So, the state of a ferroelectric crystal can generally be characterized macroscopically by two order parameters, polarization and strain. It is the coupling between the order parameters, polarization and strain, and the thermodynamic variables such as temperature, stress, and electric field that leads to the multifunctionality of a ferroelectric crystal ranging from dielectric, piezoelectric to pyroelectric properties, and thus to many applications in a wide variety of electronic devices, including capacitors, actuators, nonvolatile memories, and microelectromechanical systems. Although the thermodynamics of these couplings has been well established, the coupling among order parameters and their gradients is much less well understood. The main goal of this proposed program is to fundamentally understand the role of the flexoelectric effect, the coupling between polarization and the gradient of strain in the ferroelectricity of a crystal, in domain structures, polarization distributions across domain walls, and domain switching. There is sufficient evidence that the flexoelectric effect, which is small and generally ignored in macroscopic systems, may become significant or even dominant with decreasing size approaching nanostructures, particularly in ferroelectric materials which exhibit strong dielectric properties. The PI plans to employ a phase-field modeling approach integrated with mesoscale elasticity and electrostatic theory. The main objectives of this proposal are: (1) to develop a phase-field model of ferroelectric domain structures and switching incorporating flexoelectric contributions, (2) to study whether the flexoelectric contribution can significantly modify the properties of a ferroelectric domain wall and to discover potentially new domain wall features induced by the flexoelectric effect, (3) to investigate the role of the flexoelectric contribution to the polarization distribution and thus to domain structure in thin films, and (4) to investigate the flexoelectric response of ferroelectric thin films under a local mechanical force and explore the possibility of mechanical switching of ferroelectric polarization. The proposed research is expected to: (1) yield a phase-field formulation for modeling flexoelectric response of ferroelectrics, (2) significantly contribute to the fundamental understanding of the roles of flexoelectric effect in ferroelectric properties including domain wall structures, polarization distribution, and switching, and (3) produce advanced numerical algorithms based on the spectral method for solving phase-field equations involving domain wall anisotropy and flexoelectricity. The project will contribute to human resource development by training both graduate and undergraduate students through undergraduate thesis and summer research. The research findings will be disseminated to a wide audience through archival publications and conferences, review papers, and active participation and lectures at workshops and conferences. Finally, the PI will actively pursue collaborations with industry and national labs such as Los Alamos, Argonne, Oak Ridge, and the industrial members associated with the Center for Dielectrics and Piezoelectrics (CDP) at North Carolina State University and Penn State to provide internship opportunities for students involved in the project.